## 1. IntroductionSince 1980, the solutions giving the position of the equator of the Earth cannot be computed with only a theory of the rigid Earth. The IAU 1980 adopted nutation series are deduced from the Kinoshita (1977) theory of the rotation of the rigid Earth, by convolution with the non-rigid Earth's transfer functions of Wahr (1981). By using modern techniques like Very Long Baseline Interferometry (VLBI) precession and nutations may be presently observed with a precision of about 20 as. The differences between the theory and the observation must reveal only the effects of the non-rigidity of the Earth, so it is necessary to build a theory of the rigid Earth with a precision better than 2 as. In Bretagnon et al. (1997) we have built analytical solutions for each of the Earth's three Euler angles , using truncated solution for the motion of the Moon. Over 1900-2050, the precision was 16 as for , 8 as for and 15 as for . For improving our solution we have computed geocentric rectangular coordinates of the Moon referred to the ecliptic and equinox J2000 from the complete solution ELP 2000 (Chapront-Touzé, Chapront, 1983). Also we have computed the right-hand sides of the equations with a better accuracy. © European Southern Observatory (ESO) 1998 Online publication: November 24, 1997 |